Nahua mushroom gatherers use area-restricted search strategies that conform to marginal value theorem predictions Luis Pacheco-Cobosa,1,2, Bruce Winterhalderb, Cecilia Cuatianquiz-Limac, Marcos F. Rosettid, Robyn Hudsond, and Cody T. Rosse,1 aCuerpo Academico´ Biolog´ıa y Ecolog´ıa del Comportamiento, Facultad de Biolog´ıa, Universidad Veracruzana, Xalapa, Veracruz 91090, Mexico; bGraduate Group in Ecology, Department of Anthropology, University of California, Davis, CA 95616; cCentro Tlaxcala de Biolog´ıa de la Conducta, Universidad Autonoma´ de Tlaxcala, Tlaxcala 90062, Mexico; dInstituto de Investigaciones Biomedicas,´ Universidad Nacional Autonoma´ de Mexico,´ Mexico City 04510, Mexico; and eDepartment of Human Behavior, Ecology and Culture, Max Planck Institute for Evolutionary Anthropology, Leipzig 04103, Germany Edited by Kristen Hawkes, University of Utah, Salt Lake City, UT, and approved April 5, 2019 (received for review August 22, 2018) We develop a method of analysis for testing the marginal value contrast, are composites of intensive (low speed and high turning theorem (MVT) in natural settings that does not require an inde- rate) and extensive (high speed and low turning rate) search peri- pendent definition or mapping of patches. We draw on recent ods (21). Simulation models suggest that encounter-conditional theoretical work on area-restricted search (ARS) that links turning- ARS can be more efficient than unconditional L´evy flights or angle and step-size changes to geographically localized encounter- Brownian walks with equal average movement velocities (e.g., rates. These models allow us to estimate “giving-up times” using ref. 22), but little work has explored how ARS parameters can encounter-annotated GPS tracking data. Applied to a case study of be effectively tuned, or how the insights of the MVT literature Nahua mushroom foragers, these models identify distinct forms of can be applied to models of foraging in continuous rather than intrapatch and interpatch search behavior, with intrapatch search discrete environments. transitioning to interpatch search after a predictable interval of Here, we use a model of adaptive, encounter-conditional time since the last encounter with a harvested mushroom. Our search heuristics to link the MVT and ARS literatures. We empirical estimate of giving-up time coincides with the theoreti- demonstrate that the MVT provides numerical predictions for ANTHROPOLOGY cally optimal giving-up time derived under the MVT in the same the optimal number of time-step lags for which a slow and tor- environment. The MVT is currently underused in studies of human tuous ARS should be enacted following an encounter. We then foraging and settlement patterns, due in large part to the diffi- draw on a database of encounter-annotated GPS data—GPS culty of identifying discrete resource patches and quantifying their tracks paired with GPS waypoints on the time and location of characteristics. Our methods mitigate the need to make such dis- food item encounters—recorded during focal follows of Nahua crete maps of patches and thus have the potential to broaden mushroom foragers searching in a natural setting. These data APPLIED the scope for empirical evaluations of the MVT and related the- are used to fit a Bayesian model of encounter-conditional ARS ory in humans. Beyond studies of naturalistic foraging in humans MATHEMATICS and other animals, our approach has implications for optimiza- tion of search behavior in a range of applied fields where search Significance dynamics must be adapted to shifting patterns of environmental heterogeneity affecting prey density and patchiness. Using GPS trackers, we followed Nahua mushroom collec- tors to study how experienced foragers efficiently search area-restricted search j marginal value theorem j tracking j GPS j for resources. Locating patchily distributed resources while Levy´ flight reducing traveling costs requires a forager to balance time spent searching for new patches and searching within known oragers whose optimal search mode entails mobility (1) must patches. We present an analytical model of foraging behav- Finvest some fraction of their limited energy budget in active ior in which foragers can detect and change the way they search for randomly and often sparsely distributed (2) food items search by adjusting direction and speed as a function of time or natural resources. This active mode of search can require a since last resource encounter. This model can be used to test substantial expenditure of energy (1, 3), increase exposure to theoretical predictions concerning how long foragers should environmental hazards and predators (4), and entail the opportu- remain inside a given patch. Elucidating how organisms effi- nity costs of separation from a home base or social group. As such, ciently search is of widespread interest across academic dis- understanding how mobile foragers increase resource encounter- ciplines: the potential applications of the method explained rates has been central to a variety of foraging models in evolu- here range from conservation biology to robotic design. tionary biology, with applied consequences for fields as diverse as criminology (5), cognitive science (6), engineering (7), conserva- Author contributions: L.P.-C. designed research; L.P.-C., B.W., C.C.-L., M.F.R., R.H., and tion biology (8, 9), and agricultural pest management (10). Early C.T.R. performed research; C.T.R. analyzed data; and L.P.C., B.W., and C.T.R. wrote the empirical work inspired by the marginal value theorem (MVT) paper.y (11) focused on models of patch choice (12, 13) and patch- The authors declare no conflict of interest.y residence times (14, 15). More recent work, drawing on increased This article is a PNAS Direct Submission.y computational resources, has focused on identifying efficient This open access article is distributed under Creative Commons Attribution-NonCommercial- random walk search algorithms (16–19)—e.g., for Brownian NoDerivatives License 4.0 (CC BY-NC-ND).y walks, L´evy flights, and area-restricted search (ARS)—which can Data deposition: The data and code supporting our analysis have been stored on Github model a forager’s movement patterns even in cases where patch (https://github.com/ctross/mushrooming).y choice and patch-residence times are hard to measure. 1 L.P.-C. and C.T.R. contributed equally to this work.y Brownian walk search patterns can be nonoriented and dif- 2 To whom correspondence should be addressed. Email: [email protected] fusive (e.g., dispersal), or oriented and superdiffusive (e.g., This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. migration), while L´evy flight search patterns are scale-free, 1073/pnas.1814476116/-/DCSupplemental.y nonoriented, and superdiffusive (20). ARS search patterns, in Published online May 6, 2019. www.pnas.org/cgi/doi/10.1073/pnas.1814476116 PNAS j May 21, 2019 j vol. 116 j no. 21 j 10339–10347 trajectories. The empirical estimates of “giving-up time” impediment to empirical tests and technological applications of (GUT)—a measure of “intrapatch” search duration—from this the MVT (41). Methods of analysis that mitigate the need to model are numerically concordant with predictions of the same make a discrete map of patches have the potential to broaden the quantity derived from the MVT. More generally, we illustrate scope for empirical evaluations of the MVT and related theory a method of analysis for testing the MVT in natural settings (e.g., ref. 50). that does not require an independent definition or mapping of patches—expanding the empirical scope of the MVT to cases Integrating ARS Models and the MVT to Explain the Search Pat- where quantitative data on patch boundaries and their respective terns of Nahua Mushroom Foragers. To generalize the insights of food item densities are unavailable or impossible to obtain. the MVT to the case of sessile food items that are distributed continuously over an environment with spatial autocorrelation Theory on Search in Continuous Environments (i.e., patchiness), we use recent mathematical and statistical ARS. A central focus in movement ecology is how mobile preda- approaches developed in the ARS literature (19, 22, 26, 34) to tors can most efficiently locate randomly distributed food items. estimate the number of time-step lags for which turning-angle A body of literature on the L´evy flight foraging hypothesis has and step-size changes are associated with encounters with food suggested that foragers should search for randomly distributed items. We use encounter-annotated GPS data to make these esti- food items using approximations to L´evy flights (18, 23, 24), since mates. The number of time-step lags for which these effects are they are frequently more efficient than Brownian movement significant multiplied by the length of each time-step yields an at encountering sparse, randomly distributed food items. More estimate of the GUT (42, 51) for a local patch (22). Although recent work on intermittent and two-stage search has exam- GPS tracks annotated with behavioral observations on encoun- ined how encounters with food items (22, 25, 26) can trigger ters with food items can themselves be difficult to acquire, such ARS behavior (27–34) in which search velocity and turning- data have been collected in nonhuman animals using clever angle (35) are modified for some interval of time. This work research designs (e.g., refs. 29 and 30), as well as in humans (e.g., demonstrates that foragers of patchily distributed resources can ref. 34); increasingly powerful and simple-to-use GPS units will use a simple heuristic—search with slower and more tortuous undoubtedly make production of such data easier. movement after a recent encounter with a food item (intrapatch In the following sections, we first introduce the field-site search) and move with more rapid and linear movement otherwise and foraging context. After this, we provide the mathemati- (“interpatch” search)—to improve search efficacy.